Nonlinear optical devices have required a non-centrosymetric crystal which has non-zero components of the second order polarizability tensor. Under intense laser radiation of suitable wavelength the crystal can produce nonlinear optical effects such as second harmonic generation (SHG), sum frequency generation (SFG), difference frequency generation (DFG) and optical parametric amplification (OPA), via the .chi..sup.(2) type nonlinear process. Devices utilizing these effects have been described in U.S. Pat. Nos. 3,262,058 and 3,328,723.
The nonlinear optical conversion efficiency of the SHG process at moderate input laser power is given by: EQU Formula (1) EQU .eta.=(I.sub.2.omega. /I.sub..omega.)=C*L.sup.2 *[d.sub.eff ].sup.2 *I.sub..omega. *sinc.sup.2 [.DELTA.kL/2] (1)
where
I.sub.2.omega. =intensity of second harmonic wave PA1 I.sub..omega. =intensity of fundamental wave PA1 d.sub.eff =the effective value of nonlinear susceptibility PA1 L=length of crystal PA1 C=constant term PA1 .DELTA.k=phase mismatch=k.sub.2.omega. -2k.sub..omega. PA1 n.sub..omega..spsb.o =refractive index if the ordinary fundamental wave PA1 n.sub.2.omega..spsb.o =refractive index of the ordinary second harmonic wave PA1 n.sub.2.omega..spsb.e =refractive index of the extraordinary second harmonic wave PA1 .theta.=phase matching angle relative to the optic axis (for uniaxial crystals)
This linear relationship is valid when only a small amount of the incident radiation is converted to a different wavelength. When the phase mismatch between the two waves is .pi. the conversion efficiency is zero. The length of crystal over which this happens is referred to as the coherence length, and is typically of the order of 20 .mu.m. Maximum conversion efficiency is obtained when the phase matching condition is achieved where .DELTA.k=0 and sinc(.DELTA.kL/2)=1. In this situation the second harmonic and fundamental waves stay in phase as the fundamental propagates in the crystal and the conversion efficiency is proportional to L.sup.2. Phase matching is realized when the refractive index of the fundamental and second harmonic waves are equal and is therefore only allowed in birefringent crystals.
Two types of phase matching have been used. Type I is where the two fundamental waves are of the same polarization; and Type II where the two fundamental waves are of orthogonal polarization.
Four techniques can be employed to achieve phase matching (see U.S. Pat. No. 3,949,323, which is incorporated by reference). In the most commonly used angle tuning method the nonlinear crystal is rotated to obtain phase matching. Temperature and pressure tuning may also be introduced as well as application of stress.
Practical applications in nonlinear devices using the angle tuning method are restricted by the walk-off effect. Double refraction causes a difference in the propagation direction and direction of energy propagation for the extraordinary wave. The result is a separation of the fundamental and second harmonic waves with propagation through the crystal. The walk-off angle is described by: EQU Formula (2) EQU tan(.rho.)=(n.sub..omega..spsb.o /2)*{1/(n.sub.2.omega..spsb.e).sup.2 -1/(n.sub.2.omega..spsb.o).sup.2 }*sin (2.theta.) (2)
where
A second limiting effect is phase mismatch resulting from the divergence of the incident fundamental laser beam. Phase mismatch is interpreted in terms of the acceptance angle, which describes the deviation angle about the phase matching direction where the intensity of the second harmonic is one half the maximum intensity. The half width angular acceptance angle is given by: EQU Formula (3) EQU .delta..theta..sub.1/2 =.lambda..sub..omega. /(L[n.sub.2.omega..spsb.o -n.sub.2.omega..spsb.e ]*sin2.theta.) (3)
where EQU .lambda..sub..omega. =wavelength of the fundamental wave EQU L=crystal length
Formula (2) shows that minimum walk-off occurs when .theta.=90.degree., i.e. when the propagation direction is in a plane perpendicular to the optic axis. Similarly, the largest angular acceptance occurs at this angle, where the second harmonic intensity is most insensitive to angular deviations. The situation where .theta.=90.degree. is referred to as the non-critical phase matching (NCPM) condition. NCPM is possible when the natural dispersion of the nonlinear crystal offsets the birefringence. Temperature tuning can be utilized to achieve NCPM when the phase matching angle is close to 90.degree., as in crystals with small birefringence.
For optically biaxial crystals phase matching is described in terms of both .theta. and .phi. which are polar angles of the propagation direction of the fundamental wave. Acceptance angles are measured in both .theta. and .phi. and the smallest is conventionally defined as the limiting acceptance angle of the nonlinear crystal.
At present, there are several crystals commonly used in nonlinear optical devices. KH.sub.2 PO.sub.4 (KDP), (NH.sub.2).sub.2 CO (Urea), KTiOPO.sub.4 (KTP), LiNbO.sub.3, and more recently the borate crystals BaB.sub.2 O.sub.4 (BBO) and LiB.sub.3 O.sub.7 (LBO). Each class of crystals have advantages but also disadvantages. KDP and Urea are hygroscopic(water soluble) and have small acceptance angles. KTP and LiNbO.sub.3 show relatively large nonlinearity but are unable to phase match in the UV region and the damage threshold is low. Both the borates are capable of producing harmonics in the deep UV but their d.sub.eff is very small. RbNbB.sub.2 O.sub.6 (RNB) and its related isomorphs may overcome some of the shortcomings of those materials.
The crystal structure of RNB was first reported in Mat. Res. Bull. 10, 469, (1975). It was assigned to orthorhombic Pnm2.sub.1 space group with the mm2 point group. One year later, the same authors made correction in Acta. Cryst. B32, 2211 (1976) to reassign it being monoclinic and space group Pn. The lattice parameters were respectively for a=3.928.times.5 .ANG., b=9.449 .ANG. and c=7.389 .ANG., .alpha.=90.00.degree. and Z=10 in each unit cell. RNB was synthesized accidently in very small (sub-milimeter) size of crystal. These authors made no reference to the potential nonlinear optical properties of the crystal or the related isomorphs. The current inventors were the first to grow sizable high quality single crystals and the first to use these RNB crystals to demonstrate nonlinear optical behavior.